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Volume Growth Estimates of Gradient Ricci Solitons [PDF]

Journal of Geometric Analysis, 2022
In this paper, we survey the volume growth estimates for shrinking, steady, and expanding gradient Ricci solitons. Together with the known results, we also prove some new volume growth estimates for expanding gradient Ricci solitons.
Pak-Yeung Chan
exaly   +2 more sources

On the Topological Classification of Four-Dimensional Steady Gradient Ricci Solitons with Nonnegative Sectional Curvature

Mathematics
In this paper, we study the topology of steady gradient Ricci solitons with nonnegative sectional curvature. We apply a characterization theorem for the fundamental group of a positively curved steady gradient Ricci soliton that admits a critical point ...
Yuehan Hao
doaj   +2 more sources

Rigidity of Non-Steady Gradient Ricci Solitons

Axioms
Let (M,g) be a connected, compact Riemannian manifold of dimensionan n. We demonstrate that, after a suitable normalization, a shrinking gradient Ricci soliton (M,g,f,λ) is trivial exactly when the mean value of f is less than or equal to n2.
Mohammed Guediri
doaj   +2 more sources

O(2)-symmetry of 3D steady gradient Ricci solitons [PDF]

Geometry & Topology, 2022
For any 3D steady gradient Ricci soliton with positive curvature, we prove that it must be isometric to the Bryant soliton if it is asymptotic to a ray. Otherwise, it is asymptotic to a sector and hence a flying wing. We show that all 3D flying wings are
Y. Lai
semanticscholar   +1 more source

Kähler gradient Ricci solitons with large symmetry [PDF]

Advances in Mathematics, 2023
Let $(M, g, J, f)$ be an irreducible non-trivial K\"{a}hler gradient Ricci soliton of real dimension $2n$. We show that its group of isometries is of dimension at most $n^2$ and the case of equality is characterized. As a consequence, our framework shows
Hung Tran
semanticscholar   +1 more source

Four-dimensional steady gradient Ricci solitons with 3-cylindrical tangent flows at infinity [PDF]

Advances in Mathematics, 2021
In this paper we consider 4-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed 4-manifold. In particular, we study
R. Bamler, B. Chow, Yu-Xing Deng, Zilu Ma, Yongjia Zhang   +4 more
semanticscholar   +1 more source

h-Almost Ricci–Yamabe Solitons in Paracontact Geometry

Mathematics, 2022
In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient ...
Uday Chand De, Mohammad Nazrul Islam Khan, Arpan Sardar   +2 more
doaj   +1 more source

Gradient Ricci–Yamabe Soliton on Twisted Product Manifolds

Journal of Mathematics, 2022
In this paper, we study the twisted product manifolds with gradient Ricci–Yamabe solitons. Then, we classify and characterize the warped product and twisted product spaces with gradient Ricci–Yamabe solitons.
Byung Hak Kim, Jin Hyuk Choi, Sang Deok Lee, Chang Yong Han   +3 more
doaj   +1 more source

On harmonic and biharmonic maps from gradient Ricci solitons [PDF]

Mathematische Nachrichten, 2022
We study harmonic and biharmonic maps from gradient Ricci solitons. We derive a number of analytic and geometric conditions under which harmonic maps are constant and which force biharmonic maps to be harmonic. In particular, we show that biharmonic maps
V. Branding
semanticscholar   +1 more source

A study on conformal Ricci solitons and conformal Ricci almost solitons within the framework of almost contact geometry

Karpatsʹkì Matematičnì Publìkacìï, 2023
The goal of this paper is to find some important Einstein manifolds using conformal Ricci solitons and conformal Ricci almost solitons. We prove that a Kenmotsu metric as a conformal Ricci soliton is Einstein if it is an $\eta$-Einstein or the potential ...
S. Dey
doaj   +1 more source